Boundary values as Hamiltonian variables. I. New Poisson brackets

Details Boundary values as Hamiltonian variables. I. New Poisson brackets Boundary values as Hamiltonian variables. I. New Poisson brackets

1993-05-25

arxiv.org/abs/hep-th/9305133v1

J.Math.Phys. 34 (1993) 5747-5769

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LaTex, IHEP 93-48

Scientific paper

10.1063/1.530280

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift this restriction. The new brackets generalize a canonical bracket considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary problem in hydrodynamics. Our definition of Poisson brackets permits to treat boundary values of a field on equal footing with its internal values and directly estimate the brackets between both surface and volume integrals. This construction is applied to any local form of Poisson brackets. A prescription for delta-function on closed domains and a definition of the {\it full} variational derivative are proposed.

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